Research
Research interests
My current research lies at the intersection of mathematical physics, nonlinear partial differential equations, and probability. I am especially interested in the effective dynamics and structure of many-body systems when the system size is intractably large and a reduction in complexity is needed to answer basic questions.
Physics is a rich source of these problems—for example, Coulomb and Riesz gases—and my recent work also develops connections with statistics and machine learning.
My research is funded in part by the National Science Foundation through grants DMS-2441170, DMS-2345533, and DMS-2342349.
Work in preparation
- With M. Delgadino and R. Gvalani. Sharp two-sided size-of-chaos estimates for equilibrium gases with singular interactions.
- With M. Delgadino and R. Gvalani. Sharp mean-field estimates for diffusive log/Riesz gases.
- With K. Mun. The optimal spectral gap for the noisy synchronized Kuramoto model.
- With A. Chodron de Courcel. The gradient flows of sub-Coulomb Riesz energies.
- With E. Hess-Childs and S. Serfaty. Optimal quantization for Riesz MMDs.
- Optimal modulated logarithmic Sobolev inequality and generation of chaos for the Kuramoto model.
- With A. Chodron de Courcel and S. Serfaty. Exact solvability of the macroscopic circular log gas.
- With J. Huang and S. Serfaty. Regularity and decay estimates for confined and unconfined mean-field equations.
- With J. Huang and S. Serfaty. Fluctuations around the mean-field limit for noisy singular Riesz flows.
- With A. Hannani, G. Staffilani, and M.B. Tran. On a transport-diffusion equation originating in wave turbulence theory.
Collaborators
Shrey Aryan, Antonin Chodron de Courcel, Matías G. Delgadino, Rishabh Gvalani, Amirali Hannani, Elias Hess-Childs, Jiaoyang Huang, Dana Mendelson, Joseph K. Miller, Kyunghoo Mun, Andrea R. Nahmod, Quoc-Hung Nguyen, Nataša Pavlović, Sylvia Serfaty, Dejan Slepčev, Gigliola Staffilani, Minh-Binh Tran, and Lihan Wang.
The research blog is intended in part to make active directions visible before the associated papers are complete. If something here intersects with your work or suggests a direction we might pursue together, please get in touch.